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Geometric Series

2. Geometric Series. Section 1.6B. Key Terms. A geometric sequence is a list of numbers that have a COMMON RATIO ( r ) meaning you DIVIDED by the same number. To find r = DIVIDE THE SECOND NUMBER TO THE FIRST NUMBER Series – The TOTAL of a sequence.

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Geometric Series

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  1. 1.6: Geometric Series

  2. 1.6: Geometric Series

  3. 1.6: Geometric Series

  4. 1.6: Geometric Series

  5. 2 1.6: Geometric Series

  6. 1.6: Geometric Series

  7. Geometric Series Section 1.6B 1.6: Geometric Series

  8. Key Terms • A geometric sequence is a list of numbers that have a COMMON RATIO (r) meaning you DIVIDED by the same number. • To find r = DIVIDE THE SECOND NUMBER TO THE FIRST NUMBER • Series – The TOTALof a sequence. • Sigma Notation: . If you do not recognize the pattern, you could plug in ALL the numbers from the bottom (first) to the top (last), evaluate each one, then add them up. • Geometric Mean is the central number in a geometric progression 1.6: Geometric Series

  9. 5 ∑ 5(2)n–1 n =1 5 5 + 10 + 20 + 40 + 80 = ∑ 5(2)n n = 1 Sigma Notation Is read as: “the sum from n equals 1 to 5 of 5 times 2 to the n power.” upper limit of summation lower limit of summation index of summation 1.6: Geometric Series

  10. Formulas Geometric Sum: 1.6: Geometric Series

  11. Formulas Sigma Form of Geometric Series: 1.6: Geometric Series

  12. Example 1 Write in Sigma Notation, 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 1.6: Geometric Series

  13. Example 2 Write in Sigma Notation, 5, 15, 45, … 885735. Hint, use your calculator 1.6: Geometric Series

  14. Your Turn Write in Sigma Notation for this Geometric Sequence, 21, 15, 75/7, … 1875/343. 1.6: Geometric Series

  15. Example 3 Find the following sum for following geometric series, 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 1.6: Geometric Series

  16. Your Turn Find the following sum for following geometric series, –1/3, 1/9, –1/27, 1/81, –1/243, 1/512 1.6: Geometric Series

  17. Example 4 Evaluate 1.6: Geometric Series

  18. Example 4 Evaluate 1.6: Geometric Series

  19. Example 5 Evaluate 1.6: Geometric Series

  20. Your Turn Evaluate 1.6: Geometric Series

  21. Geometric Mean E. Geometric Mean is the central number in a geometric progression F. Formula: , where A and B are the numbers given 1.6: Geometric Series

  22. Example 6 Determine the Geometric Mean of ½ and 1/32. 1.6: Geometric Series

  23. Your Turn Determine the Geometric Mean of 2√3 and 4√5. Leave answer in Radical Form. 1.6: Geometric Series

  24. Assignment Worksheet 1.6: Geometric Series

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